This invention relates to a digital filter and, in particular, to a digital filter of linear phase non-recursive type.
A digital audio system generally makes use of an analog low pass filter in order to remove the high frequency components contained in the output of the digital-analog converter. FIG. 1 shows a circuit block diagram in such a case, a frequency characteristic diagram being shown in FIG. 2. In general, a low pass filter is required with a characteristic shown by the dotted line E so that the source signal A is passed but high frequency components B, C and D are attenuated. It is not a desirable method, however, to make use of a filter with such steep characteristics because distortions will be caused in the high frequency part of the audio signals.
For this reason, a digital filter is usually disposed before the digital-analog converter as shown in FIG. 3. If the higher harmonics component B which is closest to the normal playback range can be eliminated or if a digital filter with the characteristics shown by the dotted line F of FIG. 4 can be used, the result will be as shown in FIG. 5, there remaining only higher harmonics C which can be eliminated with an analog low pass filter with a relatively gentle frequency characteristic G. Thus, the distortion of waveforms can be minimized and high fidelity reproduction becomes possible.
FIG. 6 shows the circuit structure of a conventional digital filter of non-recursive type with its output sampling frequency twice as large as the input sampling frequency. In FIG. 6, delay elements D.sub.1. . . D.sub.13 have a same delay time T, A.sub.1. . . A.sub.14 are coefficients, m.sub.1. . . m.sub.14 are multipliers and a is an adder. If the digital filter is of linear phase type, the following relationships hold among the coefficients: A.sub.1 =A.sub.14, A.sub.2 =A.sub.13, A.sub.3 =A.sub.12, A.sub.4 =A.sub.11, A.sub.5 =A.sub.10, A.sub.6 =A.sub.9 and A.sub.7 =A.sub.8.
The usual method of making the output sampling frequency of such a digital filter twice that of the input sampling frequency so that its characteristics will be as shown by the dotted line F of FIG. 4 (and that, for example, a band with its center at 44.1 KHz will be attenuated but another band with its center twice that value, or 88.2 KHz, as well as the source signal A will pass) is to insert zero data between the input data of the digital filter once every time period of T. If this method is used, the input data of even-numbered multipliers m.sub.2, m.sub.4 . . . m.sub.14 become 0 at certain time t and those of odd-numbered multipliers m.sub.1, m.sub.3 . . . m.sub.13 become 0 at time (t+T) as shown in FIG. 6.
In order to reduce the number of multipliers by a factor of 2, a circuit composition shown in FIG. 7 may now be considered. At time t, the seven multipliers m.sub.1. . . m.sub.7 respectively execute multiplications of coefficients A.sub.1, A.sub.3, A.sub.5, A.sub.7, A.sub.9, A.sub.11 and A.sub.13 with the output data from the delay elements while at time (t+T) they execute multiplications of coefficients A.sub.2, A.sub.4, A.sub.6, A.sub.8, A.sub.10, A.sub.12 and A.sub.14 with the output data from the delay elements. Thus, by executing multiplications of odd-numbered and even-numbered coefficients alternately, the same output can be obtained as that by using the digital filter of FIG. 6. However, the number of multiplications cannot be reduced any further.
In general, multiplications take more time than additions and subtractions. If the time required for each multiplication is to be reduced, the hardware will become complicated and expensive. For this reason, it is extremely important to reduce the frequency of multiplications in the data processing of a digital audio system.